Question

By law, the maximum slope of a wheelchair ramp is 1/12.

a. A ramp is designed that is 4 feet high and has horizontal length of 50 feet. Does this ramp meet the law? Explain.

b. What could be adjusted on a unacceptable ramp so that it meets the law?

Answer 1

`\bf slope\implies \cfrac{\stackrel{\stackrel{rise}{height}}{4}}{\stackrel{\stackrel{run}{base}}{50}}\implies \cfrac{2}{25}\\e \cfrac{1}{12} \\\\\\ \textit{one could adjust the height}\qquad \cfrac{h}{50}=\cfrac{1}{12}\implies h=\cfrac{50}{12}\implies h=4(1)/(6) \\\\\\ \textit{or one could adjust the base}\qquad \cfrac{4}{b}=\cfrac{1}{12}\implies 48=b`

Answer 2

Slope is defined as rise (height) over run (length) so we can express this as slope = Height/Length.

Your rule says that the maximum slope (H/L) cannot exceed 1/12. If the height is 4 this means the length must be at least 4(12) = 48.

In other words: slope = H/L = 4(1)/4(12) = 4/48 = 1/12

If L is less than 48 the the slope is Greater than 1/12 and this is not allowed. Any length longer than 48 and the slope is less than 1/12 and this is OK.

Since 50 > 48 the ramp will be acceptable